Learning Statistics with R - A tutorial for psychology students and other beginners, 2018a

for the difference “(mean 1) minus (mean 2)”, which will be the reverse of what you’d get if you were
calculating the confidence interval for the difference “(mean 2) minus (mean 1)”.
Okay, that’s pretty straightforward when you think about it, but now consider our t-test comparing
Anastasia’s class to Bernadette’s class. Which one should we call “mean 1” and which one should we
call “mean 2”. It’s arbitrary. However, you really do need to designate one of them as “mean 1” and the
other one as “mean 2”. Not surprisingly, the way that R handles this is also pretty arbitrary. In earlier
versions of the book I used to try to explain it, but after a while I gave up, because it’s not really all that
important, and to be honest I can never remember myself. Whenever I get a significant t-test result, and
I want to figure out which mean is the larger one, I don’t try to figure it out by looking at the t-statistic.
Why would I bother doing that? It’s foolish. It’s easier just look at the actual group means, since the R
output actually shows them!
Here’s the important thing. Because it really doesn’t matter what R printed out, I usually try to
report the t-statistic in such a way that the numbers match up with the text. Here’s what I mean...
suppose that what I want to write in my report is “Anastasia’s class had higher grades than Bernadette’s
class”. The phrasing here implies that Anastasia’s group comes first, so it makes sense to report the
t-statistic as if Anastasia’s class corresponded to group 1. If so, I would write
Anastasia’s class had higher grades than Bernadette’s class (tp31q “2.1,p“ .04).
(I wouldn’t actually underline the word “higher” in real life, I’m just doing it to emphasise the point that
“higher” corresponds to positive t values). On the other hand, suppose the phrasing I wanted to use has
Bernadette’s class listed first. If so, it makes more sense to treat her class as group 1, and if so, the write
up looks like this:
Bernadette’s class had lower grades than Anastasia’s class (tp31q “´2.1,p“ .04).
Because I’m talking about one group having “lower” scores this time around, it is more sensible to use
the negative form of the t-statistic. It just makes it read more cleanly.
One last thing: please note that you can’t do this for other types of test statistics. It works for t-tests,
but it wouldn’t be meaningful for chi-square testsm F -tests or indeed for most of the tests I talk about
in this book. So don’t overgeneralise this advice! I’m really just talking about t-tests here and nothing
else!
13.3.8 Assumptions of the test
As always, our hypothesis test relies on some assumptions. So what are they? For the Student t-test
there are three assumptions, some of which we saw previously in the context of the one sample t-test (see
Section 13.2.3):
• Normality. Like the one-sample t-test, it is assumed that the data are normally distributed. Specifically,
we assume that both groups are normally distributed. In Section 13.9 we’ll discuss how to
test for normality, and in Section 13.10 we’ll discuss possible solutions.
• Independence. Once again, it is assumed that the observations are independently sampled. In the
context of the Student test this has two aspects to it. Firstly, we assume that the observations
within each sample are independent of one another (exactly the same as for the one-sample test).
However, we also assume that there are no cross-sample dependencies. If, for instance, it turns
out that you included some participants in both experimental conditions of your study (e.g., by
accidentally allowing the same person to sign up to different conditions), then there are some cross
sample dependencies that you’d need to take into account.
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